SOLUTION: [sqrt(3+sqrt5)] - [sqrt(3-sqrt5)]^2 = 2
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Question 1117379: [sqrt(3+sqrt5)] - [sqrt(3-sqrt5)]^2 = 2
Answer by solver91311(24713) (Show Source): You can put this solution on YOUR website!
The statement given is not true because you are only squaring the 2nd term in the left-hand side. If, as I suspect, you actually meant the problem to read:
^2\ =^? \ 2)
Then the proof is given below.
Expand the binomial in the LHS
\ -\ 2\(\sqrt{3\ +\ \sqrt{5}}\)\(\sqrt{3\ -\ \sqrt{5}}\)\ +\ \(3\ -\ \sqrt{5}\)\ =^?\ 2)
Collect like terms and calculate the product of conjugates in the center term of the LHS
\ =^?\ 2)
\ \equiv\ 2)
John
My calculator said it, I believe it, that settles it
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